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Abstract

Muqarnas is an iconic element of Islamic architecture. It exhibits fascinating beauty
and captures the attention of viewers via its complicated form and mesmerizing patterns.
Generating a 3D model of a muqarnas and designing the patterns to decorate
it have applications in architecture, virtual tourism and other areas. Modeling virtual
muqarnas can be very challenging, requiring a lot of time and eff ort even from
expert modellers. Our goal is to provide an analysis of muqarnas and its decorating
patterns as well as a set of methods and tools which can facilitate the modeling of
muqarnas.
In this thesis, we present a new approach to model muqarnas. Our approach is
to consider muqarnas as a transition between layers of di fferent form. We also take
advantage of a special type of ceiling plan, called two dimensional pattern plans, as a
guide to overcome the complexity of the muqarnas. Using these methods we provide
an interactive framework to design muqarnas.
Muqarnas structures are frequently decorated with diff erent patterns. Among
these patterns, Persian
oral patterns are very interesting but poorly studied. We
provide a novel method to generate Persian
oral patterns to decorate our models.
The key idea in this method is to decompose the patterns into the ornaments and the
composition and secondly, separating the geometry from the combinatorial properties
of the composition.
Our implementation of the presented methods is a software tool that can generate
complicated muqarnas models. Several examples of virtual models, including models
of real buildings as well as new designs made using this software, are shown.